Possible improvements of the interaction energy calculated using minimal basis sets

Interaction energies for H₂O·H₂O, H₂O·F^– and H₂O·CH₄ have been calculated using the LCAO MO SCF method with minimal basis sets, and employing the counterpoise method to eliminate the basis set superposition error. The results compare favourably with those obtained using extended basis sets. It is shown that for H₂O·H₂O and for the benzene-carbonyl cyanide complex a large part of the dispersion energy can easily be obtained as a sum of bond-bond dispersion energies calculated from a London-type formula using experimental values of the bond polarizability tensors. By considering the interaction between a water and a glycine molecule it is also shown that the dispersion energy plays an important role in the hydration of organic molecules.On leave from the Quantum Chemistry Laboratory, Institute of Basic Problems of Chemistry, University of Warsaw, Pasteura 1, 02-093 Warsaw, Poland     

Minimal basis sets in calculations of intermolecular interaction energies

Several minimal (7, 3/3) Gaussian basis sets have been used to calculate the energies and some other properties of CH₄ and H₂O. Improved basis sets developed for these molecules have been extended to NH₃ and HF and employed to H₂CO and CH₃OH. Interaction energies between XH_n molecules have been calculated using the old and the new minimal basis sets. The results obtained with the new basis sets are comparable in accuracy to those calculated with significantly more extended basis sets involving polarization functions. Binding energies calculated using the counterpoise method are not much different for the new and the old minimal basis sets, and are likely to be more accurate than the results of much more extended calculations.     

Overestimation of the coupling component in the CP technique. Application of the indirect counterpoise correction to the H2O?HF hydrogen-bonded system

An extension of the Indirect Counterpoise (ICP) method, proposed in previous work, has been applied to the H₂O? HF hydrogen-bonded system. The new version, which introduces important numerical changes is called EICP (Extended Indirect Counterpoise method). In their framework, the nonnegligible overestimation of the Counterpoise correction (CP) of Boys and Bernardi in the coupling component (MIX) of the interaction energy, computed via the Kitaura and Morokuma method is studied. Several basis sets, BS, were used to describe the oxygen, fluorine and hydrogen atoms that constitute the complex. The EICP results leads to more coherent values with the uncorrected energy than with the CP correction, which seems to be significantly affected by the size and type of the basis set used (especially for minimal basis sets).     

Removal of dependencies from nearly complete basis sets. Calculations on the helium dimer

A method is devised for dealing with almost linearly dependent basis sets that contain large sets of bond functions. Using the largest of such basis sets, LARSAT, the second-order Møller-Plesset polarization dispersion energy of the helium dimer is calculated to be - 17.08 K at R = 5.6 bohrs. MR-SDCI calculations, employing a set of 37 reference configurations, were performed for the helium dimer with several basis sets at 4.0 and 5.6 bohrs. Size-extensivity corrections were included to take into account the R dependency of the size-extensivity error in MR-SDCI calculations. The He₂ interaction energies computed with basis LARSAT are - 10.92 K at 5.6 bohrs and 295.1 K at 4.0 bohrs. The 37-MR-SDCI calculations with basis LARSAT almost reproduce the He₂ full configuration interaction (CI) interaction energies computed with the same basis, at notably smaller cost. © 1997 John Wiley & Sons, Inc. Int J Quant Chem 63: 805–815, 1997     

Ab-initio studies of fluoroxytrifluoromethane geometry and electronic structure

Ab-initio molecular orbital calculations using both minimal or STO-3G and extended or 4-31G basis sets have been applied to fluoroxytrifluormethane. Complete geometry optimizations using both basis sets have been applied to this molecule and the calculated structural parameters have been compared to the electron diffraction data. The extended basis set calculations are found to be in much better overall agreement with experiment although the minimal basis set does reproduce the angular parameters well, including the tilt angle. The barrier to the CF₃ torsion has been computed and it compares favorably with the microwave spectral value.The electronic structure of CF₃OF and some related molecules have been examined by partitioning the electrons according to the method of Mulliken. The highest occupied orbital in CF₃OF is found to be largely an O-F π * orbital and the O-F bond is also found to be the least ionic and weakest bond in the molecule. The computed dipole moment of CF₃OF agrees well with the experimental value.     

Can extrapolation to the basis set limit be an alternative to the counterpoise correction? A study on the helium dimer

Configuration interaction and coupled cluster calculations are reported for He₂ using various orbital basis sets of the d-aug-AVXZ type, with the results being extrapolated to the one electron basis set limit both with counterpoise and without counterpoise correction. A generalized uniform singlet- and triplet-pair extrapolation scheme has been utilized for such a purpose. Using appropriate corrections to mimic full configuration interaction, the energies were predicted in excellent agreement with the best available estimates. The results also suggest that extrapolation to the complete basis set limit may be a general alternative to the counterpoise correction that yields a more accurate potential energy while being more economical.     

Self-assembly of DMF with chloromethane and their structures: a theoretical study

The stability of hydrogen-bonded complexes, DMF–H _n CCl_4−n (n = 1–3), has been investigated by several theoretical methods including the MP2 level of ab initio theory at various basis sets from 6-31+G* to 6-311++G**. Two stable configurations (respectively a and b) were obtained for each complex with no imaginary frequencies. The minimum energy structure of these complexes has also been analyzed by means of the atoms in molecule theory at MP2/6-311++G** level. It is found that C–H···O hydrogen bonding exists in these systems and that the intensity of HB interaction gradually increases with successive chlorination. Computed results indicate that these complexes automatically assemble into different stable configurations. For the complexes under consideration, their stabilities can be mainly ascribed to the intermolecular HB interaction. The present work is helpful to clearly understand the interaction mechanism of these complexes in theory.     

A minimal model of potential energy surface for H2O?HCl

In this paper, we present a model of potential energy surface for the H₂O HCl system, consisting in the exact transformation of quantum chemical input data related to a minimal number of significant configurations. Both molecules are assumed as rigid. The interaction potential is given by an expansion in real spherical harmonics depending on the distance between the two centers of mass of the molecules and on four angles that define their mutual orientation. The main target of this work is the construction of a model of potential energy surface that requires a limited number of single energy points, which is suitable for applications to classical and quantum molecular dynamics simulations, permitting interpolation and further implementation of different sets of input data.     

Ab initio study of the structure,cooperativity, and vibrational properties in the mixed hydrogen‐bonded trimers of hydrogen isocyanide and water

The five trimers of H₂O···HNC···H₂O, H₂O···H₂O···HNC, HNC···H₂O···H₂O, H₂O···HNC···HNC, and HNC···HNC···H₂O have been studied with quantum chemical calculations. Their structures, harmonic vibrational frequencies and interaction energies have been calculated at the B3LYP and MP2 levels with the aug‐cc‐pVDZ and aug‐cc‐pVTZ basis sets. The cooperative effect on these properties has also been studied quantitatively. For HNC:(H₂O)₂ systems, the cyclic H₂O···H₂O···HNC trimer is most stable with an interaction energy of ?16.01 kcal/mol and a large cooperative energy of ?3.25 kcal/mol at the MP2/aug‐cc‐pVTZ level. For H₂O:(HNC)₂ systems, the interaction energy and cooperative energy in the H₂O···HNC···HNC trimer are larger than those in the HNC···HNC···H₂O trimer. The NH stretch frequency has a blue shift for the terminal HNC molecule in the HNC···H₂O···H₂O and HNC···HNC···H₂O trimers and a red shift in other cases. A many‐body analysis has also been performed to understand the interaction energies in these hydrogen‐bonded clusters. © 2010 Wiley Periodicals, Inc. Int J Quantum Chem, 2011     

Multireference basis-set reduction

We review “Hilbert space basis-set reduction” (BSR) as an approach to reduce the computational effort of accurate correlation calculations for large basis sets. We partition the single-particle basis into a small “internal” and a large “external” set. We use the MRCI method for the calculation for that part of configuration space in which only internal orbitals are occupied and perturbatively correct for the remaining configurations using a method similar to Shavitt's B_k method. The present implementation approximates the MRCI result for the unpartitioned basis set, with a significantly reduced computational effort. To demonstrate the viability of the method, we present results for selected states of small molecules (Be₂, CH₂, O₃). For the examples investigated, we find that relative energy differences can be reproduced to an accuracy of approximately 1 kcal/mol with a significant computational saving. © 1996 John Wiley & Sons, Inc.     

On the validity of complete basis set extrapolation formula optimized for the equilibrium distance applied to the potential energy surface for the correlation energy of the helium dimer

Full configuration interaction calculations are performed for He₂ using various orbital basis sets of the aug‐cc‐pVXZ type, with the correlation energies being extrapolated to the complete basis set (CBS) limit. A two‐point CBS extrapolation formula has been utilized for such a purpose. It is shown that the extrapolation formula with the offset parameter k(R) optimized for the equilibrium distance is not uniformly applicable to He He distances in the very short region of the potential energy curve. The offset parameter k(R) in the repulsive region of the potential energy curve can be largely different with the one in the long‐range distances especially in the cases of basis‐sets with large cardinality number. It is also noticed that the accuracy of this extrapolation scheme may not be improved with the increasing of the cardinality number.     

Intermolecular potential energy surface for CS2 dimer

A new four‐dimensional intermolecular potential energy surface for CS₂ dimer is obtained by ab initio calculation of the interaction energies for a range of configurations and center‐of‐mass separation distances for the first time. The calculations were performed using the supermolecular approach at the Møller–Plesset second‐order perturbation (MP2) level of theory with the augmented correlation consistent basis sets (aug‐cc‐pVxZ, x = D, T) and corrected for the basis‐set superposition error using the full counterpoise correction method. A two‐point extrapolation method was used to extrapolate the calculated energy points to the complete basis set limit. The effect of using the higher levels of theory, quadratic configuration interaction containing single, double, and perturbative triple excitations QCISD(T) and coupled cluster singles, doubles and perturbative triples excitations CCSD(T), on the shape of potential energy surface was investigated. It is shown that the MP2 level of theory apparently performs extremely poorly for describing the intermolecular potential energy surface, overestimating the total energy by a factor of nearly 1.73 in comparison with the QCISD(T) and CCSD(T) values. The value of isotropic dipole–dipole dispersion coefficient (C₆) of CS₂ fluid was obtained from the extrapolated MP2 potential energy surface. The MP2 extrapolated energy points were fitted to well‐known analytical potential functions using two different methods to represent the potential energy surface analytically. The most stable configuration of the dimer was determined at R = 6.23 au, α = 90°, β = 90°, and γ = 90°, with a well depth of 3.980 kcal mol^?1 at the MP2 level of theory. Finally, the calculated second virial coefficients were compared with experimental values to test the quality of the presented potential energy surface. © 2010 Wiley Periodicals, Inc. J Comput Chem, 2011.     

Basis set effects on Cu(I) coordination in Cu-ZSM-5: a computational study

DFT calculations on the coordination of Cu⁺ to the framework oxygen atoms of Al-substituted ZSM-5 were performed by using combinations of different basis sets in order to investigate the dependence of the results on the adopted computational level. With low-end basis sets, a large basis set superposition error (BSSE) favors the coordination of Cu⁺ to three to four oxygen atoms of the framework, only two of which belong to the AlO₄ tetrahedron corresponding to the investigated T-site. More extended basis sets considerably lower the BSSE and favor the coordination of Cu⁺ to only two oxygen atoms of the AlO₄ tetrahedron. Upon interaction with NO, the Cu⁺ ion is always coordinated by two oxygen atoms of the AlO₄ tetrahedron, independently of the basis set adopted and of the coordination number before NO adsorption. The shift from three- to twofold coordination caused by the Cu⁺–NO interaction requires a deformation energy that lowers the final adsorption energy. Such an effect is relevant with low-end basis sets, whereas it is substantially absent with more extended basis sets, which favor the twofold coordination of Cu⁺ even before NO adsorption. As a result, high-end basis sets increase the NO interaction energy with respect to that calculated by low-end basis sets, in agreement with experiments and suggesting a possible re-interpretation of the catalytic properties of the investigated sites. Provided suitable scale factors are employed, the N–O stretching frequencies of adsorbed nitrogen oxide calculated by sufficiently extended basis sets turned out in fair agreement with experimental findings.     

Ab initio studies on several species of the formula X3YO and X3YOH

Ab initio molecular orbital calculations using both minimal and extended basis sets have been applied to two isoelectronic sets of molecules. One set corresponds to the 18 electron species H₃NO, H₃CO^– and H₃COH while the second set contains the 42 electron fluorinated molecules F₃NO, F₃CO^– and F₃COH. The geometries of these molecules have been optimized, using both the minimal STO-3G and the extended 4-31G basis sets. These comparative calculations reveal that the 4-31G basis produced structural parameters in much better agreement with experiment. The effect of includingd-orbitals in the basis set was also investigated. For the fluorinated oxides it has been found that the optimized 4-31G structures were only slightly altered by the addition ofd-orbitals. For H₃NO, on the other hand, the inclusion ofd-orbitals considerably shortens the N-O bond distance. Both H₃NO and CF₃OH, which are unknown experimentally, are theoretically predicted to be capable of existence. The electronic structures of these molecules have also been examined using electronic partitioning according to the Mulliken scheme.     

A method for population and bonding analyses in calculations with extended basis sets

Summary A method for population and bonding analyses in the calculations with extended basis sets is proposed. The definition and evaluation method of the atomic orbitals in molecular environments (AOIMs) are described. It is shown that the AOIMs can be divided into two subsets, the strongly occupied minimal compact subset {AOIM}_B and the very weakly occupied “Rydberg” subset {AOIM}_R, according to the orbital population obtained from Mulliken analysis with AOIMs as basis sets. The viewpoint of “molecular orbitals consisting of minimal atomic orbital sets” can be optimally realized in terms of {AOIM}_B. The Mulliken population based on AOIMs is reasonable and fairly stable to changes of basis sets. The Mayer bond orders calculated based on {AOIM}_B are quite stable to the changes of basis sets; therefore they can be used to measure objectively the contribution of individual atomic orbitals to bonding.     

Water trimer cation

By using density functional theory (DFT) and high-level ab initio theory, we have investigated the structure, interaction energy, electronic property, and IR spectra of the water trimer cation [(H₂O) ₃ ⁺ ]. Two structures of the water trimer cation [the H₃O⁺ containing linear (3Lp) structure versus the ring (3OO) structure] are compared. For the complete basis set (CBS) limit of coupled cluster theory with single, double, and perturbative triple excitations [CCSD(T)], the 3Lp structure is 11.9?kcal/mol more stable than the 3OO structure. This indicates that the ionization of water clusters produce the hydronium cation moiety (H₃O⁺) and the hydroxyl radical. It is interesting to note that the calculation results of the water trimer cation vary seriously depending on the calculation level. At the level of M?ller?CPlesset second-order perturbation (MP2) theory, the stability of 3OO is underestimated due to the underestimated O??O hemibonding energy. This stability is also underestimated even for the CCSD(T) single point calculations on the MP2-optimized geometry. For the 3OO structure, the MP2 and CCSD(T) calculations give closed-ring structures with a hemi-bond between two O atoms, while the DFT calculations show open-ring structures due to the overestimated O??O hemibonding energy. Thus, in order to obtain reliable stabilities and frequencies of the water trimer cation, the CCSD(T) geometry optimizations and frequency calculations are necessary. In this regard, the DFT functionals need to be improved to take into account the proper O??O hemibonding energy.     

Theoretical Study on Intermolecular Interactions and Thermodynamic Properties of Difluoroamine Complex

Introduction　　ApplicationsofabinitiocalculationstointermolecularinteractionsincludingeitherweakvanderWaalsorstrongerhydrogenbondinghavedrawnmuchattentioninthepastdecadesbecausetheyareimportantinawiderangeofphysical,chemicalandbiologicalfields .1 5Inre centyears ,wehaveappliedtheintermolecularinteractionstoenergeticsystemsandobtainedsomemeaningfulinfor mationthatisvaluableforthestudyofenergeticmateri als .6 14 Thebehaviorofmolecularcomplexesisusuallybe tweentwoextremes :thegasphaseandthecrys…